TIDES

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TIDES
Tide - generic term to define alternating rise
and fall in sea level with respect to land and
is produced by the balance between the
gravitational acceleration (of the moon and sun
mainly) and the centrifugal acceleration.
Tide also occurs in large lakes, in the
atmosphere, and within the solid crust
Gravitational Force (Newtons Law of
Gravitation) F GmM/R2 G 6.6710-11 N
m2/kg2
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How strong is the Tide-Generating Force?
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How strong is the Tide-Generating Force?
The mass of the sun is 2x1027 metric tons while
that of the moon is only 7.3x1019 metric tons.
The sun is 390 times farther away from the
earth than is the moon. The relative Tide
Generating Force on Earth (2x1027/7.3x1019)/(3
903) or 2.7x107/5.9x107 0.46 or 46
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What alters the range and phase of tides produced
by Equilibrium Theory?
Non-astronomical factors coastline
configuration bathymetry atmospheric forcing
(wind velocity and barometric pressure) hydrogra
phy may alter speed, produce resonance effects
and seiching, storm surges
In the open ocean, tidally induced variations of
sea level are a few cm. When the tidal wave
moves to the continental shelf and into confining
channels, the variations may become greater.
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Keep in mind that tidal waves travel as shallow
(long) waves
How so?
Typical wavelengths 4500 km (semidiurnal wave
traveling over 1000 m of water)
Ratio of depth / wavelength 1 / 4500
C gH 0.5
Then, their phase speed is
The tide observed at any location is the
superposition of several constituents that arise
from diverse tidal forcing mechanisms.
Main constituents
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The Form factor F K1 O1 / M2 S2 is
customarily used to characterize the tide.
When 0.25 lt F lt 1.25 the tide is mixed - mainly
semidiurnal
When 1.25 lt F lt 3.00 the tide is mixed - mainly
diurnal
F gt 3 the tide is diurnal
F lt 0.25 the tide is semidiurnal
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Superposition of constituents generates
modulation - e.g. fortnightly, monthly
This applies for both sea level and velocity
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Subtidal modulation by two tidal constituents
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In Hampton Roads M2 0.72 m N2 0.16 m O1
0.08 m S2 0.13 m K1 0.10 m F K1 01 /
S2 M2 0.21
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From Pinet (1998)
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Co-oscillation
Independent tide - caused by gravitational and
centrifugal forces directly on the waters of a
basin -- usually negligible effect for typical
dimensions of semienclosed basins
Co-oscillating tide - caused by the ocean tide at
the entrance to a basin as driving force
The wave propagates into the basin and may be
subject to RESONANCE and RECTIFICATION -- alters
tidal flows and produces subtidal motions
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Standing Waves
Half-wave oscillator
Quarter-wave oscillator
Natural standing wave (lake, harbor, estuary)
---- seiche
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Mode 1 (n 1)
Merions Formula
Shoreline convergence might be more important
than resonance in producing tidal amplification
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Effects of Rotation on a Progressive Tidal Wave
in a Semi-enclosed basin
R C / f
KELVIN WAVE
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Effects of Rotation on a Standing Tidal Wave in a
Semi-enclosed Basin
Two Kelvin waves of equal amplitude progressing
in opposite directions.
Instead of having lines of no motion, we are now
reduced to a central region --- amphidromic
region-- of no motion at the origin. The
interference of two geostrophically controlled
simple harmonic waves produces a change from a
linear standing wave to a rotary wave.
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Two Kelvin Waves in Opposite Directions
Distance (m)
Distance (m)
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Two Kelvin Waves in Opposite Directions
km
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Effects of Bottom Friction on an
amphydromic system
(Parker, 1990)
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Virtual Amphidromes
(Parker, 1990)
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Virtual amphidromes in Chesapeake Bay